The present invention is directed to instruments used to measure positional changes of two objects that are movable relative to one another, using quite varied physical scanning principles. A distinction is made between photoelectric, magnetic, inductive and capacitive scanning. The basic principle is the same for all the methods, however, wherein a periodic measuring graduation is scanned, and the scanning signal thus generated is evaluated as a measurement signal.
The period of the scanning signals obtained is determined by the period or increment of graduation of a graduation-bearing substrate. In photoelectric measuring instruments, the increment is determined by the width of a transparent strip and an opaque strip in the measuring direction. Upon the relative motion between a scanning unit and the measurement graduation of the graduation-bearing substrate, one counting pulse is derived from each scanned increment and added together with the correct algebraic sign, and the sum is available as a measured value.
The periodic analog signals obtained from the graduations of the graduation-bearing substrate in photoelectric, magnetic, inductive and capacitive measuring instruments generally do not have a purely sinusoidal form; instead, they include harmonics, resulting for example from inaccuracies in the graduations. These graduation inaccuracies result from different spacings of the transparent and opaque strips, for instance, or from a lack of sharpness at the edges of these strips. To keep the analog signals obtained predominantly free of harmonics, stringent demands for accuracy of the graduations must be made. If accurate position measurement values for each graduation period are to be made, and if exact subdivision of the graduation periods by forming interpolated values are to be possible in order to increase the resolution further, then the analog signal obtained from this graduation must be free of harmonics. The formation of subdivisions through interpolated values derived by means of a computer, for instance, is described in German Published, Non-Examined Patent Application DE- OS 27 29 697.
Measuring instruments are also known that furnish triangular or trapezoidal analog signals, which intrinsically always include harmonics.
German Patent 19 41 731 discloses a photoelectric length measuring instrument, in which a frequency filter aperture with a sinusoidal shape of permeability is provided to obtain a harmonics-free analog signal when the graduation of a graduation-bearing substrate is scanned. In this measuring instrument, a special frequency filter aperture must be manufactured and installed. In addition, this measuring instrument is limited to the photoelectric transmitted-light measuring principle, in which a strip system made up of periodic fluctuations in brightness is generated, by the so-called vernier principle or moire effect.
To obtain harmonics-free periodic signals, German Patent Disclosure 32 39 108 C2 proposes ascertaining the bandwidth (number of frequencies or waves) of the analog signal by scanning the period of the graduation with various scanning elements and subjecting the periodic analog signals furnished by the scanning elements to a Fourier analysis. Such a Fourier analysis allows one to ascertain Fourier coefficients of the fundamental of the analog signal, and evaluating the Fourier coefficients as harmonics-free periodic signals to form position measurement values.
A mathematically equivalent, but completely different embodiment of the principle of harmonics filtration is known as so-called arcsin scanning, disclosed in DE 34 12 128 C1. An intensity distribution (grating pattern in the shadow, or self-reproduction in the Talbot plane) is created by a first grating, and is scanned with a grating of variable graduation. The disadvantage is that the ideal distribution of the arcsin scanning graduation varies, depending on the total number of graduation lines.